(36g) A Simulation-Based Derivative-Free Optimization Framework Using the Kinetic Monte Carlo Method for Controlling Polymer Molecular Weight and Sequence Distribution Synthesized Via Free Radical Polymerization

The diversity of the potential arrangements of multiple monomers along the length of polymer chains and their impact on polymer properties spark interests in the design of polymer sequence characteristics for particular applications^1,2. Kinetic Monte Carlo (KMC) is a technique that can track the explicit arrangement of monomers in the polymer chains, and recently there have been developments that significantly improve the calculation speed of KMC simulations^3,4. Yet it is still difficult to integrate with conventional gradient-based optimization algorithms that are typically invoked to design polymer properties, because KMC does not supply derivative information directly as a stochastic simulation algorithm.

In this work, we developed an optimization framework based on a derivative-free method that incorporates KMC simulations to efficiently find synthesis conditions for property targets, including molecular weight and sequence. The derivative-free optimization algorithm is named Bounded Optimization BY Quadratic Approximation (BOBYQA) developed by Powell⁵. This algorithm finds the minimum of a differentiable “black box” function calculated from the output of a KMC simulation, which we have adopted to return properties of a polymer for given synthesis conditions.

The performance of our model is demonstrated on a copolymerization system of butyl acrylate (BA) and methyl methacrylate (MMA) in a batch reactor. We show by two case studies that the model can accurately and efficiently control molecular weight and sequence targets by changing reaction conditions such as temperature, monomer composition and overall conversion. The algorithm can also provide insight on designing reactivity ratios to better meet the property targets. In addition, the explicit sequence information generated from KMC allows for detailed analysis and control of the distribution of sequence characteristics among different chains.

Reference

1. Iedema PD, Hoefsloot HC. Synthesis of Branched Polymer Architectures from Molecular Weight and Branching Distributions for Radical Polymerisation with Long‐Chain Branching, Accounting for Topology‐Controlled Random Scission. Macromolecular Theory and Simulations. 2001;10(9):855-869.

2. Van Steenberge PHM, D’hooge DR, Wang Y, et al. Linear Gradient Quality of ATRP Copolymers. Macromolecules. 2012;45(21):8519-8531.

3. Gao H, Oakley LH, Konstantinov IA, Arturo SG, Broadbelt LJ. Acceleration of Kinetic Monte Carlo Method for the Simulation of Free Radical Copolymerization through Scaling. Industrial & Engineering Chemistry Research. 2015;54(48):11975-11985.

4. Tripathi AK, Sundberg DC. A Hybrid Algorithm for Accurate and Efficient Monte Carlo Simulations of Free-Radical Polymerization Reactions. Macromolecular Theory and Simulations. 2015;24(1):52-64.

5. Powell MJ. The BOBYQA Algorithm for Bound Constrained Optimization without Derivatives. Cambridge Report 2009/06, University of Cambridge, Cambridge. 2009.